Help with freehand drawing and editing

Hi! I'm trying to create a logo by tracing a bitmap of cursive-style writing and using the vector points to refine it. My problem is that I was trying to avoid having to create white shapes to make the openings in letters like e and cursive l, for example. So I tried making the shape as if I was actually writing it, i.e. looping the line around over itself. But wherever the 'lines' overlap, the color goes away, like they're canceling each other out. Is there another way to do this, or is there some conversion that needs to be done? Thanks!

the pen tool(s) incorporate a setting for excluding an area, it's the little icon w/ a hollow box over a filled box, IIRC, on your tool bar. what you need to do is select the pen, trace the outline of your letter, then select the "subtract from area" icon and trace the outline of the inner opening.